The diocese of Segorbe-Castellon said in a statement the monk was from the Order of "Los Carmelitas Descalzos" and his superiors had taken action against him.
It did not name the monk, nor give details of the charges against him. Nobody at the diocese was available to comment.
"The Bishop expresses his dismay over the acts reported to the police which, if true, are unacceptable for Church and society," the statement said.
"He shares the pain of the victim, his parents and family and asks them for forgiveness," the statement said. "Not a single case of abuse by a priest is acceptable."
Several Spanish media said the Order had transferred the monk to a convent in northern Spain and banned him from being alone with children as a precautionary measure.
Media also reported that the order had passed on details of the suspected case to the public prosecution of the Supreme Court in Valencia, but no one was available at the court to comment on the reports.
Although the number of practicing Catholics in Spain is waning, the Catholic Church remains influential in society and has many supporters in the main opposition Popular Party (PP).
Pope Benedict said this month the sexual abuse scandal shaking Roman Catholicism showed the Church needed to do penance for its sins.
Critics have accused the Pope and the Church of mishandling and even covering up sexual abuse of children by priests in the United States, Ireland, Germany, Italy and elsewhere.
SIC: Reuters